NECESSARY AND SUFFICIENT CONDITIONS FOR THE STABILIZATION OF A SOLUTION TO THE DIRICHLET PROBLEM FOR PARABOLIC EQUATION

摘要

We obtain necessary and sufficient conditions for the stabilization to zero of the solution to the Dirichlet problem for a nondivergence parabolic equation with measurable coefficients. The conditions are formulated in terms of the divergence of Wiener series containing the heat capacity introduced by E. M. Landis. In the case of the heat equation, these conditions yield the stabilization criterion.